A wireless W-band 3D-printed temperature sensor based on a three-dimensional photonic crystal operating beyond 1000 ∘C

In addressing sensing in harsh and dynamic environments, there are no available millimeter-wave chipless and wireless sensors capable of continuous operation at extremely high temperatures. Here we present a fully dielectric wireless temperature sensor capable of operating beyond 1000 ∘C. The sensor uses high-Q cavities embedded within a three-dimensional photonic crystal resonating at 83.5 GHz and 85.5 GHz, and a flattened Luneburg lens enhances its readout range. The sensor is additively manufactured using Lithography-based Ceramic Manufacturing in Alumina (Al2O3). Despite the clutter, its frequency-coded response remains detectable from outside the furnace at 50 cm and at temperatures up to 1200 ∘C. It is observed that the resonance frequencies shift with temperature. This shift is linked to a change in the dielectric properties of Al2O3, which are estimated up to 1200 ∘C and show good agreement with literature values. The sensor is thus highly suitable for millimeter-wave applications in dynamic, cluttered, and high-temperature environments.

Supplementary Note S3: Setup for temperature measurements The measurement setup employed for the temperature measurements is presented in Supplementary Figure 4.The sensor -formed by the 3D photonic crystal with the flattened lens on top -was placed inside the furnace.A fan was added for cooling, as it was found that the springs holding the furnace's door closed softened up after approximately 1000 • C.This implied that the door opened slightly, which could potentially heat up the measuring antenna.
The effectivity of the fan on keeping the measurement equipment at room temperature was confirmed via multiple measurements with a thermal camera.
For automatic measurements, voltage out of the furnace's thermopar was measured with a voltmeter, and the temperature was estimated by reading out the corresponding voltage and comparing it to calibration curves of voltage versus temperature previously established.MATLAB was used to automatize the process.

Supplementary Discussion S4: Range readout estimation
As presented in the main body of the publication, the readout range of the sensor with our measurement setup is limited to 1 m at room temperature and to approximately 0.5 m at 1200 • C, which is a short range for indoor applications.However, its measured radar cross-section is of −20 dB m 2 , which can be employed to predict the readout range when changing system parameters such as the reader's antenna gain, sensitivity, transmitted power, etc.
The maximum readout distance for the sensor can be estimated by employing the radar range equation (Eq.1).
On this equation, ∆P stands for the difference between the transmitted power and the received power without a sensor, ∆P = P t /P rx, no sensor .The minimum value for P rx, no sensor is determined by the noise floor of the reader.I.e., ∆P describes the available dynamic range of the measurement equipment.Then, γ min accounts for a minimum required contrast between the backscattered power by the sensor and the noise floor, so the sensor can be accurately detected, γ min = P rx, sensor /P rx, no sensor .Finally, G describes the transmitter/receiver antenna gain, λ corresponds to the operating wavelength and σ is the radar cross-section of the sensor.
One simple approach to extend the readout range, according to Eq. 1, involves raising G, where each 6 dB increase doubles the preceding readout range.The horn antenna employed in our measurement setup has a G of 23 dBi, whereas the W-band lens antenna in [1] has 35 dBi.Furthermore, commercially available Cassegrain reflector antennas reach values of 50 dBi and higher.Supplementary Figure 5 presents the maximum readout distance of the sensor against the coefficient ∆P/γ min , representing the results for the aforementioned antennas.This maximum range is presented for the temperature range between room temperature (T = 21 • C) and the maximum measured temperature (T = 1200 • C), as the increased dielectric losses with temperature decrease the sensor's backscattered power by approximately 7 dB.
For our measurement setup, ∆P = 70 dB, while γ min is set to 10 dB to guarantee a large enough contrast between the sensor's frequency peaks and the noise floor.It is noticeable the short R max when the horn antenna in our laboratory is employed (blue lines), of 0.75 m for T = 1200 • C.However, this increases rapidly when the considered antenna is the aforementioned lens antenna or Cassegrain reflector antenna, to 3.5 m and 18 m, respectively.It should be mentioned that the maximum readout distance can also be increased by decreasing the noise floor.For example, the clutter suppression method detailed in [2] decreases the noise floor by 10 dB compared to time-gating, and thus increases the product ∆P/γ min by 10 dB (dashed gray line in Fig. 5).R max P Supplementary Discussion S5: Estimation of τ t An estimation of the time required for the sensor to react to temperature changes is given in this section, assuming that the sensor is in contact with solid metallic surfaces on its sides.Further, it is assumed that this metal and Alumina have perfect thermal conductivity and that there is no heat radiation in the environment, so that the heat transfer occurs only at the metal-ceramic interface.
When the environment increases its temperature ∆T , the sensor temperature exponentially increases over time according to [3]: With T 0 the initial temperature and τ t the time constant of the sensor.Further, ρ corresponds to the density of the ceramic, c p to the specific heat, V the sensor's volume, h c the interfacial heat transfer conductance at the metalceramic interface and A s the contact surface area between the metallic parts and the sensor.
Assuming 99 % Al 2 O 3 , the values of the previous parameters are ρ = 3890 kg cm −3 , c p = 880 J kg −1 K −1 and h c varies between 1500 W m −2 K −1 to 8500 W m −2 K −1 , depending on the surface finishes and pressure between the metal and ceramic [3].
In order to estimate τ t , some assumptions are made.First, the lens is excluded from these calculations, as the shift in f res regarding temperature occurs when the cavities (and hence the PhC structure) are heated up.Second, due to its large porosity, the PhC has a filling factor, η fill of 11.26 %.Hence, V is calculated as V = η fill • V block , where V block corresponds to the volume of the PhC if it was completely solid.Do note that this simplification assumes that there are no input waveguide or cavities implemented within the PhC CONTENTS structure.Third, it is assumed that several sides of the PhC are enclosed by a thin Alumina slab, which in turn is in contact with a metallic plate.This is a feasible situation in reality, as the three-dimensional electromagnetic bandgap isolates the cavities from external influences, as mentioned in the main publication.
With these assumptions, four different cases are used to calculate τ t , following the sketch in Supplementary Figure 6.
1.Only the bottom side of the PhC is in contact with metal.2. The bottom side and two of the opposite sides of the PhC act as heating sources.3.All sides (but for the one on which the lens is placed) are in contact with metal.
As τ t decreases for a larger A s , case 3 will be the one to present a smaller τ t .The results are summarized in Table 2. Following Eq. 2, for t = τ t , the difference between the temperature of the PhC and contact metal pads has been decreased by 63 %.It can be assumed that the PhC has heated up to the target temperature after 3τ t (95 %).Considering the best-case scenario (case 3), this implies that the PhC takes between 2 min to 11.8 min to heat up completely, depending on h c .
The formula above assumes that there is no convection due to heated air.However, the large porosity of the PhC implies that in real use-cases, such as during a fire or inside a turbine, the superheated air seeps in the PhC structure, allowing for a faster τ t .As a preliminary measurement, a heat gun spewing air at its medium air flow strength and 650 • C has been placed at a distance of 15 cm from the sensor.The final temperature of the sensor, measured with a thermal camera, was 125 • C. The sensor was then rapidly cooled down by switching the heat gun to operate at 50 • C, with the sensor reaching a temperature of 51 • C after 2.2 min.These results give an estimated τ t of approximately 30 s.However, do note that, to accurately measure τ t , the sensor should be placed directly in a pre-heated environment, which is currently not feasible due to the need for alignment between the PhC structure and the lens antenna.
As an observation, it is possible to decrease τ t by minimizing the coefficient V /A s , while keeping the advantages of a three-dimensional bandgap, by substituting the lens by a different antenna, such as a rod antenna.In this case, the overall volume of the PhC can be minimized, as there is no need to provide for a flat support for the lens.An example of such structure is presented in Supplementary Figure 6, where it can be appreciated that the PhC is significantly smaller.In this case, the best-case scenario following Supplementary Table 2 decreases the total heating time to 1 min, at the cost of sacrificing readout range, due to employing an antenna with a smaller aperture.Nevertheless, this showcases the different situations where this tag could be potentially used, either as a cooperative indoor radar target, or even as a temperature sensor, able to continuously operate at extremely high temperatures.

Supplementary Figure 4 :
Setup for the temperature measurements.(a) Picture showing the whole measurement setup from far away.(b) Close-up showing the sensor inside the furnace and marking the calibration plane that was employed, to remove the effect of the flexible W-band waveguide.(c) Close-up to the sensor itself, showing that the lens is placed on top, and centred, on the photonic crystal.

Table 1 :
Design parameters for the two cavities embedded within the 3D PhC